Subset neighborhood rough sets

We present a novel kind of neighborhood, named subset neighborhood and denoted asS(rho)-neighborhood. It is defined under an arbitrary binary relation using the inclusion relations between N-rho-neighborhoods. We study its relationships with some kinds of neighborhood systems given in the literature. Then, we formulate the concepts of S-rho-lower and S-rho-upper approximations, and S-rho-accuracy and roughness measures based on S-rho-neighborhoods. We show in which cases the S-rho-accuracy measure is the highest among related approximations and investigate under which conditions the S-rho-accuracy and S-rho-roughness measures are monotonic. Moreover, we compare our approach with two existing ones and elucidate the advantages of our technique to obtain accuracy measures under some specific relations. To support the obtained results, we provide two medical examples. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

We introduce a new type of neighborhood called subset neighborhood, defined under an arbitrary binary relation using the inclusion relations between N-rho-neighborhoods. We study its relationships with existing neighborhood systems and propose S-rho-lower and S-rho-upper approximations, as well as accuracy and roughness measures based on S-rho-neighborhoods. We compare our approach with existing ones and highlight the advantages in obtaining accuracy measures under specific relations. Two medical examples are provided to support the obtained results.